g versus c: comparing individual and collective intelligence across two meta-analyses

Cognitive Research: Principles and Implications

Table 5 The relationship between statistical power and observed and expected effect sizes

Power (%) by Effect Size
Study	Sample size (groups)	Small (r ≥ .10 < .30)	Moderate (r ≥ .30 < .50)	Large (r ≥ .50)	c-factor (r = .26) ^a	Mean IQ^b (r = .28)
Woolley et al. (2010 ): Study 1	40	9.4	47.7	92.0	37	41.9
Woolley et al. (2010 ): Study 2	152	23.3	96.6	100.0	90.1	93.8
Engel et al. ( 2014a b): Face-to-face (speaking) condition	32	8.4	39.2	85.3	30.3	34.3
Engel et al. ( 2014a b): Online (text-chat) condition	36	8.9	43.6	89.3	33.7	38.14
Engel et al. (2015a, b): Study 2 (Germany)	116	18.8	91.1	100.0	80.8	86.2
Engel et al. (2015a, b): Study 3 (Japan)	25	7.6	31.3	74.9	24.2	27.4
Woolley and Aggarwal (under review); (Also reported in Woolley and Aggarwal 2017)	59	11.7	64.6	98.5	51.5	57.7
Meslec, et al. (2016)	30	8.2	37.0	82.8	28.6	32.3
Glikson, Harush, et al. (under review)	115	18.6	90.8	100.0	80.4	85.9
Chikersal, et al. (2017)	58	11.6	63.9	98.4	50.8	56.9
Kim et al. ( 2017a b)	248	35.0	99.8	100.0	98.6	99.4
Aggarwal et al. (2019)	98	16.5	85.8	100.0	73.8	79.9
Barlow and Dennis (2016 )	86	15.0	81.0	99.9	68	74.4
Barlow (2015, unpublished doctoral thesis): Control Group (CG)	64	12.3	68.3	99.0	54.9	61.3
Barlow (2015, unpublished doctoral thesis): Experimental Group (EG)	65	12.4	69.0	99.2	55.6	62
Bates and Gupta (2017): Study 1	26	7.7	32.5	76.7	25.1	28.4
Bates and Gupta (2017): Study 2	40	9.4	47.7	92.3	37	41.9
Bates and Gupta (2017): Study 3	40	9.4	47.7	92.3	37	41.9
Rowe (unpublished doctoral thesis)	29	8.1	35.9	81.4	27.7	6.4
Proportion of studies with acceptable (≥ 80%) power:		0 of 19 (0%)	6 of 19 (31.2%)	17 of 19 (89%)	4 of 19 (21.1%)	4 of 19 (21.1%)

Note: Calculations of statistical power are based on the actual sample size for included studies. All power calculations are written as percentage terms (%); Categories for the magnitude of association are based on the conventions of Cohen (1988); calculations are made using G*Power 3.1 software; correlations are for bivariate normal models (Pearson's r) and computed post hoc based on alpha error probability of .05 (two-tailed) and power of 80% (1—β = .80); power calculated based on tests against a null model (r ~ 0). Sample size is based on the actual number of groups included in the study and/or condition
^aThis value is based on the sample weighted correlation derived from the meta-analysis reported in Fig. 3
^bThis value is based on a sample weighted correlation derived from three meta-analyses investigating the relationship between average (or sum) IQ scores and group performance (Bell 2007; Devine and Philips 2001; Stewart 2006)